Respuesta :
The Solution:
The correct answers are:
Curved surface area = 527.79 squared centimeters
Total surface area = 753.98 squared centimeters.
Given that the volume of a cylinder with height 14cm is
[tex]504\pi cm^3[/tex]We are required to find the curved surface area and the total surface area of the cylinder.
Step 1:
We shall find the radius (r) of the cylinder by using the formula below:
[tex]V=\pi r^2h[/tex]In this case,
[tex]\begin{gathered} V=\text{volume =504}\pi cm^3 \\ r=\text{ radius=?} \\ h=\text{ height =14cm} \end{gathered}[/tex]Substituting these values in the above formula, we get
[tex]504\pi=\pi r^2\times14[/tex]Finding the value of r by first dividing both sides, we get
[tex]\begin{gathered} \frac{504\pi}{14\pi}=r^2 \\ \\ r^2=36 \end{gathered}[/tex]Taking the square root of both sides, we get
[tex]\begin{gathered} \sqrt[]{r^2}\text{ =}\sqrt[]{36} \\ \\ r=6\operatorname{cm} \end{gathered}[/tex]Step 2:
We shall find the curved surface area by using the formula below:
[tex]\text{CSA}=2\pi rh[/tex]Where
[tex]\begin{gathered} \text{ CSA=curved surface area=?} \\ h=14\operatorname{cm} \\ r=6\operatorname{cm} \end{gathered}[/tex]Substituting these values in the formula above, we have
[tex]\text{CSA}=2\times6\times14\times\pi=168\pi=527.788\approx527.79cm^2[/tex]Step 3:
We shall find the total surface area by using the formula below:
[tex]\text{TSA}=\pi r^2+\pi r^2+2\pi rh=2\pi r^2+2\pi rh[/tex]Where
TSA= total surface area and all other parameters are as defined earlier on.
Substituting in the formula, we get
[tex]\text{TSA}=(2\pi\times6^2)+(2\pi\times6\times14)=72\pi+168\pi[/tex][tex]\text{TSA}=240\pi=753.982\approx753.98cm^2[/tex]Therefore, the correct answers are:
Curved surface area = 527.79 squared centimeters
Total surface area = 753.98 squared centimeters.
